Lance Morris has been retained in the squad and could come into contention to play in the first Test if Australia wanted extra ball speed in Nagpur while Starc is absent. Scott Boland has also retained his place in the squad as a backup seamer after losing his place in Australia's XI for the final Test against South Africa.
Chairman of selectors George Bailey said the four spinners give the squad flexibility in terms of potential partners for Lyon.
"Ashton Agar continues to impress following his comeback in Sydney and we believe left-arm finger spin will play an important role in Indian conditions," Bailey said.
"Mitchell Swepson has recent Test experience in the sub-continent and offers leg-spinning variety.
"Todd Murphy has progressed quickly having impressed in domestic cricket and recently with Australia A. With those performances Todd has emerged as a strong spin option.
"Selection in this squad also provides another opportunity to spend time alongside Nathan Lyon and assistant coach Daniel Vettori in India which will be invaluable to his development."
Handscomb's inclusion comes after he was called up to Australia's squad during the Sydney Test as cover after Harris was sent back to the BBL. Both Handscomb and Renshaw played all four Tests on Australia's last tour of India in 2017. Renshaw made two half-centuries while Handscomb made a match-saving 200-ball 72 not out in Ranchi. He has also been the leading runscorer in Sheffield Shield cricket in the past two seasons.
"Peter Handscomb deserves his place back in the squad," Bailey said. "His domestic form has been strong recently and Pete has proven he can perform at Test level.
"His experience against spin on the subcontinent is valuable and he is also an exceptionally good close to the wicket catcher."
Handscomb did cop a blow on the hip bone while batting in a Victoria T20 Super Slam game for premier club St Kilda on Tuesday night. He did retire hurt but it is understood that the injury was minor and he will be fine to tour India.
Bailey also stated that the selectors will review the squad after the second Test and could make additions given there is a seven-day break between the second Test in Delhi and the third Test in Dharamshala.
Australia squad for India tour: David Warner, Usman Khawaja, Marnus Labuschagne, Steven Smith, Travis Head, Cameron Green, Alex Carey (wk), Pat Cummins (capt), Mitchell Starc, Nathan Lyon, Josh Hazlewood, Scott Boland, Ashton Agar, Lance Morris, Mitchell Swepson, Matt Renshaw, Peter Handscomb, Todd Murphy